In this chapter we will learn to subtraction rational number with same denominators with solved examples.

We have already shown the method to **add the rational number with same denominator**. Click the red link to learn that concept.

## Subtracting rational numbers with same denominator

When we have rational numbers with same denominator, you simply have to** subtract the numerators by keeping the denominator same**.

For example, let** a/b & c/b be the rational number** with same denominator.

The subtraction is given as;

\mathtt{\Longrightarrow \frac{a}{b} -\frac{c}{b}}\\\ \\ \mathtt{\Longrightarrow \ \frac{a-c}{b}

Note that we have simply subtracted the numerator in this case.

I hope you have understood the concept. Let us now solve some problems.

**Example 01**

Subtract the rational number \mathtt{\frac{5}{3} -\frac{4}{3}} **Solution**

Note that both the rational numbers have same denominator. Hence, we will simply subtract the numerator to get the right solution.

\mathtt{\Longrightarrow \frac{5}{3} -\frac{4}{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{5-4}{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1}{3}}

Hence, **1/3 is the solution**.

**Example 02**

Subtract the numbers \mathtt{\frac{10}{7} -\frac{8}{7}}

**Solution**

\mathtt{\Longrightarrow \frac{10}{7} -\frac{8}{7}}\\\ \\ \mathtt{\Longrightarrow \ \frac{10-8}{7}}\\\ \\ \mathtt{\Longrightarrow \ \frac{2}{7}}

Hence, **2/7 is the solution.**

**Example 03**

Subtract the rational number \mathtt{\frac{4}{15} -\frac{7}{15}} **Solution**

Note that we have rational numbers with same denominator. So we will simply subtract the numerator to get the solution.

\mathtt{\Longrightarrow \frac{4}{15} -\frac{7}{15}}\\\ \\ \mathtt{\Longrightarrow \ \frac{4-7}{15}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-3}{15}}

Hence, **-3/15 is the right solution.**

**Example 04**

Subtract \mathtt{\frac{-8}{20} -\frac{9}{20}} **Solution**

Note that the rational numbers have same denominator. So we will simply subtract the numerator to get the solution.

\mathtt{\Longrightarrow \frac{-8}{20} -\frac{9}{20}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-8-9}{20}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-17}{20}}

Hence, **-17/20 is the solution.**

**Example 05**

Subtract \mathtt{\frac{-15}{13} -\frac{-19}{13}} **Solution**

Note that the multiplication of two negative numbers becomes positive.

\mathtt{\Longrightarrow \frac{-15}{13} +\frac{19}{13}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-15+19}{13}}\\\ \\ \mathtt{\Longrightarrow \ \frac{4}{13}}

Hence, **4/13 is the solution.**

**Example 06**

Subtract \mathtt{\frac{-3}{10} -\frac{2}{10}}

**Solution**

\mathtt{\Longrightarrow \frac{-3}{10} -\frac{2}{10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-3-2}{10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-5}{10}}

The rational number can be further simplified by dividing numerator & denominator by 5.

\mathtt{\Longrightarrow \ \frac{-5\div 5}{10\div 5}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-1}{2}}

Hence, **-1/2 is the right answer.**